A Christmas Miracle

Now that the holidays are here, only one thing should be on everyone’s mind; how many Christmas cookies will be waiting when we go home for break. While thinking about how I am going to gain about one hundred pounds from all the cookies I am going to eat, I was left wondering about the man, the myth, the legend, Santa Claus.  How much weight does Santa put on during his Christmas trip? How does this affect his flight?

First, I thought of Santa going on a test flight.  Assuming he has a mass of 136 kg, his sleigh has a mass of 455 kg, his bag of presents is 1,000,000 kg (he has a lot of toys) and the reindeer have a combined mass of 1,629 kg, the total mass of the system would be 1,002,220 kg. It has been estimated that Santa travels at about 1.046 x 10⁶ m/s¹. I also assume Santa has a cruising altitude of 9144m.  From this, the work of the reindeer pulling the sleigh would be (assuming the sleigh is traveling in one direction for one trip around the Earth):

W_NC = ΔKE + ΔPE

W_NC = ½ m(v_f² – v_o²) + mg(h_f – h_o)

W_NC = ½ (1,002,220kg)(1.046 x 10⁶ m/s)² + (1,002,220kg)(9.8m/s²)(9144m)

W_NC = 5.48 x 10¹⁷ J + 8.98 x 10¹⁰ J

W_NC = 5.48 x 10¹⁷ J

The force required for this would be:

F(4.01 x 10⁷m) = 5.48 x 10¹⁷ J

F = 1.37 x 10¹⁰ N

Now let’s take into account the cookies. It has been calculated that if every home Santa visited left out one chocolate cookie and one glass of milk, he would gain 6,000,000lbs or about 3,000,000kg¹ if all the calories he consumed were transformed directly to added weight!!

This incredible increase in mass without a decrease in velocity would require the work done and consequently the force exerted to increase exceptionally as well. 

Taking this all into account, the friction from air on the Santa system would be so great that no creature or toy could possibly survive.

Luckily, Santa has some Christmas magic on his side that allows him to defy the laws of physics.

Source: ¹http://www.snopes.com/holidays/christmas/santa/physics.asp